Reentrant Phase Transitions and Triple Points of Topological AdS Black Holes in Born-Infeld-Massive Gravity

Abstract

Motivated by recent developments of black hole thermodynamics in de Rham, Gabadadze, and Tolley (dRGT) massive gravity, we study the critical behaviors of topological Anti-de Sitter (AdS) black holes in the presence of Born-Infeld nonlinear electrodynamics. Here the cosmological constant appears as a dynamical pressure of the system and its corresponding conjugate quantity is interpreted as thermodynamic volume. This shows that, besides the Van der Waals-like SBH/LBH phase transitions, the so-called reentrant phase transition (RPT) appears in four-dimensional space-time when the coupling coefficients <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math> of massive potential and Born-Infeld parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:math> satisfy some certain conditions. In addition, we also find the triple critical points and the small/intermediate/large black hole phase transitions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:math>.